Orthogonal Projections on Inner Product Subspaces | Linear Algebra

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We go over orthogonal projections onto subspaces of inner product spaces. We'll see the projection theorem, telling us that - given a finite dimensional subspace W of an inner product space V, we can decompose any vector u from V into a vector in W plus a vector in the orthogonal complement W perp. We'll prove and use a theorem telling us how to calculate the orthogonal projection of a vector onto a subspace and how to calculate the component of a vector orthogonal to a subspace.

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